The signal-to-noise power ratio of a photodetector is proportional to: EQU 1/[2q(i.sub.p +i.sub.b +i.sub.d)(F.sub.e B)+4kTB/(R.sub.eq M.sup.2)](1)
where q is the electronic charge, i.sub.p is the photocurrent, i.sub.b is the background current, i.sub.d is the dark current, F.sub.e is the excess noise factor, B is the bandwidth, k is Boltzmann's constant, T is the temperature, R.sub.eq is the equivalent resistance of the load, and M is the average multiplication rate or the gain. The signal-to-noise power ratio decreases as the contributions of the first and second terms in eqn (1) increase. However, the contribution of the first term is made smaller if the excess noise factor F.sub.e decreases and the contribution of the second term, representing thermal noise, is made smaller if the gain increases. Thus, in order to increase the signal-to-noise power ratio, it is desirable to use a photodetector having low noise and high gain.
A photomultiplier tube is one of the best devices for providing low noise performance at high gain. In the photomultiplier, carrier multiplication occurs via secondary emission of electrons from metallic grids or dynodes sequentially spaced throughout the tube. The electrons can be accelerated in the vacuum to energies well above the ionization threshold while in transit between dynodes, and as a result, the gain per dynode is not limited to 2 per dynode as it is in semiconductor devices. In fact, gains between 5 and 10 per dynode are common, and overall gains can be several orders of magnitude higher than in semiconductor devices. Nevertheless, in many applications, photomultiplier have limited applicability because of their size, the high voltages required for efficient operation and the need to maintain a vacuum. Thus, there is a need for a low noise, high gain semiconductor photodetector.
Noise in any electronic device arises from fluctuations in the carrier arrival rate at the collecting contact. If no statistical fluctuations in the carrier velocities from the ensemble average velocity occur, then the carrier arrival rate, and hence the current, is completely deterministic and no noise is produced thereby. Thus, the noise of a system can be assessed by determining the variance, i.e. the average deviation from the mean, of the current.
In a p-n junction device, noise arises from the spontaneous emission and subsequent collection of independent charge carriers. An article entitled "Current Fluctuations In A Semiconductor (Dielectric) Under The Conditions Of Impact Ionization and Avalanche Breakdown," by A. S. Tager, in Sov. Phy.--Solid State, Vol. 6, pp. 1919-1925, 1965 discloses that this noise, commonly referred to as shot noise, is given by: EQU &lt;i.sub.s.sup.2 &gt;=2qB&lt;I&gt; (2)
where &lt;I&gt; is the mean collected current and B is the bandwidth.
In an avalanche photodiode, APD, additional noise arises from the fluctuation in the carrier generation rate since, in general, the carrier generation rate is not fully deterministic. In addition, fluctuations in the photon arrival rate add to the randomness in the collected current.
Tager, and later McIntyre, in an article entitled "Multiplication Noise In Uniform Avalanche Diodes," by R. J. McIntyre, IEEE Trans. Electron Dev., Vol. ED-13, 1966, pp. 164-168, demonstrated that randomness in the multiplication process produces the greatest noise when the electron and hole ionization rates are equal.
For wavelengths on the order of 1.06 um, low noise APDs can be made from silicon because the ratio of electron and hole ionization rates is large, being at least as large as 20. However, APDs which are sensitive over a large range of wavelengths are necessarily made from many different material systems, in particular from III-V semiconductor compounds and their related alloys. Unfortunately, the bulk ionization rates for electrons and holes are roughly equal in most of these materials. As a consequence, low noise, high gain photodetectors for use at long wavelengths include particular structural means for increasing the ratio of the electron and hole ionization rates over that occurring in the bulk materials from which the photodetectors are fabricated.
The following refers to semiconductor photodetectors in the prior art:
(1) An article entitled "Impact Ionization In Multilayered Heterojunction Structures," by R. Chin, N. Holonyak, G. E. Stillman, J. Y. Tang, and K. Hess, Electronics Letters, Vol. 16, 1980, pp. 467-469 discloses the use of a superlattice structure consisting of alternating thin layers of GaAs and Al.sub.x Ga.sub.1-x As in an attempt to increase the ratio of electron and hole ionization rates in a quantum well APD. It is suggested that the electron distribution is heated more than the hole distribution because of the relatively large energy difference between the conduction and valence band edge discontinuities in the specified materials and because of the difference between the electron and hole ionization mean free paths. Nevertheless, my analysis shows that because (1) the superlattice is equivalent to a spatially periodic electric field, (2) there is a strong nonlinear, i.e. exponential, dependence of "a" and "b" on the electric field, and (3) there is a threshold energy in the impact ionization process, both the electron and hole ionization rates in the superlattice are enhanced above their respective values in the bulk materials. However, the enhancement of the hole ionization rate is much less than that of the electron ionization rate for two reasons. First, because the conduction band edge discontinuity in the disclosed material system is significantly larger than the valence band edge discontinuity, electrons obtain a larger kinetic energy boost from the heterointerface between the GaAs and Al.sub.x Ga.sub.1-x As layers than do the holes. Second, and more important because the hole energy relaxation rate is much larger than the electron relaxation rate for the average carrier energies involved in the APD, the holes relax faster to their steady state energy after crossing the heterointerface than do the electrons. This results in fewer holes that "lucky-drift" to energies high enough to cause impact ionization.
(2) An article entitled "The Channeling Avalanche Photodiode: A Novel Ultra-Low-Noise Interdigitated p-n Junction Detector," by F. Capasso, IEEE Trans. Electron Dev., Vol. ED-29, 1982, pp. 1388-1395 discloses the use of a superlattice structure consisting of alternating n-GaAs and p-Al.sub.0.45 Ga.sub.0.55 As layers in another attempt to increase the ratio of electron and hole ionization rates in a channeling APD. The channeling APD is configured so that a reverse bias produces both transverse and longitudinal electric field components therein. The transverse field sweeps holes out of the GaAs layers and into adjacent Al.sub.0.45 Ga.sub.0.55 As layers while confining the electrons within the GaAs layers.
(3) An article entitled "Staircase Solid State Photomultipliers And Avalanche Photodiodes With Enhanced Ionization Rate Ratio," by F. Capasso, W. T. Tsang and G. F. Williams, IEEE Trans. Electron Dev., Vol, ED-30, 1983, pp. 381-390 discloses the use of a superlattice structure whose layers have a graded energy band gap in yet another attempt to increase the ratio of electron and hole ionization rates in a graded gap staircase APD. In such an APD, impact ionization events occur at specific and localized areas within the device, whereas, in a channeling APD impact ionization events occur randomly throughout a layer. Because impact ionization is localized in a graded gap staircase APD, the variability and, hence, the gain fluctuation of the number of electrons generated per photon is reduced. Thus, the excess noise in the graded gap staircase APD is lower than that in a conventional uniform APD and in a channeling APD. Nevertheless, a graded gap staircase APD fabricated from a GaAs/AlGaAs material system does not achieve optimum ionization localization because the conduction band edge offset between GaAs and AlGaAs is not a sufficiently large fraction of the energy bandgap in GaAs.
(4) An article entitled "Single-Carrier-Type Dominated Impact Ionization In Multilayer Structures," by H. Blauvelt, S. Margalit, and A. Yariv, Electronics Letters, Vol. 18, 1982, pp. 375-376, referred to hereinafter as Blauvelt et al discloses the use a doped superlattice structure consisting of p.sup.+ -i-n.sup.+ AlGaAs layers followed by near intrinsic GaAs and AlGaAs layers in yet another attempt to increase the ratio of electron and hole ionization rates in a quantum well APD. This structure is designed to spatially restrict the regions wherein impact ionization occurs in order to minimize the variability of the number of electrons generated per detected photon. This quantum well APD more nearly approximates photomultiplier-like behavior in regard to the localization of carrier multiplication than either the channeling APD or the graded gap staircase APD.
Blauvelt et al, however, used an unrealistically simple model of impact ionization disclosed in an article entitled "Problems Related To P-N Junctions In Silicon," by W. Shockley, Solid State Electron., Vol. 2, 1961, pp. 35-67, to analyze "a"/"b" for their APD. As a result, they recognized that the selected model, along with their qualitative design features, were inadequate tools for optimizing the design of a practical APD. Blauvelt et al stated that optimized design of the detector would necessitate calculation of the electron and hole distributions at each position as the carriers moved through the layers of the detector. Furthermore, Blauvelt et al, did not consider P the probability that an electron impact ionizes at the output of each unit of a multi-unit APD, and Q, the probability that a hole impact ionizes at the output of each unit of a multi-unit APD, in discussing the APD notwithstanding the fact that these are crucial factors to consider in providing an appropriate design for a practical APD. As a result of not considering P and Q, in addition to using a simplified model to analyze their device, Blauvelt et al completely mischaracterized the optimal, or even the appropriate parameters for a practical doped quantum well APD.
In summary, the manner in which the above-discussed devices differ is essentially the following. In the conventional APD, impact ionizations are not spatially controlled, i.e. there is no structure analogous to the dynodes of a photomultiplier. In addition, the impact ionization of secondary carriers is not suppressed, and as a result, the degree to which the secondary carriers contribute to the gain and the noise is determined solely by the material properties of the materials from which the device is fabricated. Consequently, in the conventional APD structure, GaAs is at a serious disadvantage with respect to silicon due to the nearly equal electron and hole ionization rates in GaAs. For silicon, the holes are found to have smaller impact ionization rates by a factor estimated to be about 20.
Staircase APDs, and related devices, have periodic structures which act to confine the impact ionization process to designated points in the device, so that the number of multiplications and the multiplication factor can be brought more under control, thereby reducing the output noise. In addition, the periodic structures suppress multiplication by secondary carriers and thereby improve noise performance.
In light of the above, a need exists for a low noise, high gain APD.